It is widely customary, for the different operating parts of a centrifugal machine, to provide casings having an identical shell diameter which are lined up axially in succession and which are clamped together by means of the end faces of their shells. At the same time, each casing shell includes the inner walls which govern the operation of the particular casing section. These inner walls, which define flow paths and media spaces, form sometimes complicated hollow shapes and undercut contours which can be produced by casting only at a high outlay. This is also true when the casing sections are surrounded by means of a tube absorbing the axial forces and centring the casing shells (U.S. Pat. No. 4,708,589) or stepped casings are arranged within an outer casing, leaving a functional interspace (EP-A-0 248 104). However, because there is then a larger number of casing sections, it would involve an even higher outlay, particularly in terms of stockkeeping, assembly and maintenance, to divide sections of this kind once more in order to make the cavities and undercut regions more readily accessible in the casting technique.